Name: ___________________________________
Date: _______________________________
Section 7.5 Modelling Exponential
Growth and Decay
1. Truong studied a pond where frogs lay eggs.
He found the number of tadpoles increased by
a factor of 2.43 per day. The number of
tadpoles, T, can be modelled by the relation
T = 265(2.43)t, where t is the time in days.
a) Use a graphing calculator. Graph the
relation.
b) How many tadpoles were present at the
start of Truong's study?
c) How many tadpoles were present after two
days?
d) How many tadpoles were present after one
week?
2. The graph shows the temperature in a small
South African village each hour for 10 h.
…BLM 7–10...
(page 1)
3. Late in the summer, the population of black
flies starts to decrease by 4% per day. The
population, P, can be modelled by the relation
P = 6720(0.96)t, where t is the time in days.
a) Use a graphing calculator. Graph the
relation.
b) What is the initial population of black flies?
c) What would be the population at the end of
each of the first and second weeks?
d) Approximately how long will it take for the
population to be reduced by 50%?
4. For every 5°C increase in temperature, the
length of a metal bar increases by 6%. The
length of the bar is 2.50 m at 10°C.
a) Make a table of values for this relation. Use
increments of 5°C.
b) Use a graphing calculator to make a scatter
plot of the data.
c) Find the equation of the exponential curve
of best fit.
d) Use the equation to find the temperature at
which the bar would be 4.00 m long.
a) After how long did the temperature increase
to 20°C?
b) After how long did the temperature increase
to 30°C?
c) Is it reasonable to expect that the
temperature will continue to increase?
Explain.
Foundations for College Mathematics 11: Teacher’s Resource
BLM 7–10 Section 7.5 Modelling Exponential Growth and Decay
Copyright © 2007 McGraw-Hill Ryerson Limited
Name: ___________________________________
Date: _______________________________
…BLM 7–10...
(page 2)
5. The table shows the amount remaining from a
500 mg sample of radioactive material over
time.
Time
(days)
0
1
2
3
4
5
Mass
(mg)
500
243
108
63
28
19
a) Use a graphing calculator. Plot the data and
find the equation of the exponential curve
of best fit.
b) Use the equation to find the mass
remaining after 14 days.
c) When will there be 0.001 mg remaining?
6. The table shows the world population in
billions. The year 1750 is set as t = 0.
Year
t
1750
1800
1850
1900
1950
2000
0
50
100
150
200
250
Population
(billions)
0.79
0.98
1.26
1.65
2.52
6.06
a) Make a scatter plot of the data. Find the
equation of the exponential curve of best.
b) Use the equation to estimate the population
in 2050.
c) When will the world population reach
7 billion?
7. The initial population of a bacterial culture is
2000 and the population grows at a fixed rate.
The table shows the population every hour for
6 h.
Time
(h)
0
1
2
3
4
5
6
Population
2000
2270
2614
2980
3392
3914
4456
a) Use a graphing calculator. Find the
equation of the exponential curve of best fit.
b) Use the equation to find the population of
bacteria after 12 h and after 24 h.
c) How long will it take for the population to
reach 20 000?
8. The populations, P, of the twin cities
New Oldtown (NO) and Old Newtown (ON)
can be modelled by the relations
PNO = 225 150(1.032)t and
PON = 274 500(1.026)t, where t is time in
years since 2007.
a) Use technology to determine the year in
which the populations of the two cities will
be equal.
b) What is this population?
Foundations for College Mathematics 11: Teacher’s Resource
BLM 7–10 Section 7.5 Modelling Exponential Growth and Decay
Copyright © 2007 McGraw-Hill Ryerson Limited